Chakra costs are 10x's normal in Outskirts and 100x's normal in Wasteland. As such, you're pretty much going to need to use Wasteland specific Jutsus to use any Jutsu at all.

All strength modifiers, both penalties and bonuses, do not apply in the wasteland with the exception of those few that specifically say that they do. Many wasteland allies or Jutsu carry a severe strength penalty that gets negated in the wasteland, but would apply if you tried to use it in a normal mission.

Adventuring in the wasteland costs a lot of extra stamina. It is possible to defend against Wasteland stamina drain. Protection methods include Wasteland Rebreather, A variety of wasteland cloaks (crafted), and Survived the Impossible (which completely negates stamina drain)

Because of the negation of strength bonuses, the wasteland is rather hard early on. To have any chance of success at all you will want very high range and levels.

The rest of this guide will be split into steps, each step has a variety of goals which can be achieved in any order. It is recommended that you read through an entire step before you start working on it.

Step 1 - Unlock Outskirts

Obtaining Haus is the first step to starting your wasteland adventure. To obtain Haus, you must complete Revenge. To unlock this quest, you must be a Special Jonin or higher. However, to beat this quest, you must be able to obtain 4 Gen successes at 15 difficulty with no party and very few Jutsu and you must also be Bingo'd. Don't start this mission until you know you can do both of these things.

There are two ways to pass the Gen 15d challenge. The first is to go for 4 successes and ignore the range. This is only possible if you have the +1 Gen Success NWW Item (or the Letter of Marque) and the Plug Suit monster drop from having defeated Evanjellyons. For most people, this isn't an option. The more common route is less certain: you need to get gen 15 range and hope to get 4 successes. You need at least 13 Gen range as a base (so Jonin or Sp. Jonin Genjutsu + 1 Range item is enough), and you can cover the rest with Welcome to Good Burger. If you can get 15 Gen range without Jutsu, that's even better, and you can use something like your Sword Jutsu.

Once you've completed the Gen challenge, Haus checks to make sure that you are Bingo'd Once this is done, you obtain Haus and unlock Outskirts (sometimes called "Outer Wasteland").

Step 2 - Low Level Outskirts Missions

Outskirt Items

Virtually every Outskirts mission has a drop of some kind. These drops are either ash covered items that can be appraised at the Shop, or they are various trinkets that can eventually be distilled. Almost all of these items will be useful later, but some are only useful for selling. The following items are (currently) safe to sell:

Coins and Rings used to be considered safe to sell as well, but are required in large amounts for various pizza-witch item upgrade recipes. It is possible that the remaining useless treasure items might eventually have a use.

Distilling Shafts is the fastest way to get Dust required for upgrading Hanafuda decks.

Hang onto everything else for now, you'll want to use them for creating items.

Do not recklessly appraise every item as soon as you get it. Non appraised items can be traded to other players, which is useful if you have more then you need. Some items have uses when unappraised, for example ash-covered-tile are used to upgrade your Mahjong sets. Saving up 50 unidentified items of any kind and then using "appraise all" counts as appraising 50 items at once for purpose of ally acquisition.

Appraising 50 items at once will get you the ally larry who will help increase treasure sale price by 5%, and may team up with haro (after completing wish-around-the-world) for the team bonus of doubling all item drops in the wasteland.

The "safe to sell" items listed above are all "treasure items", whose sale price varies daily at the store.

Initial Allies

The initial allies available are:

Terri won't be of much use unless you are S2+ and have her as Terri Lvl 2, in which case her +2 Tai Range/Successes will help.

Mr Sandman's effect will help soften the blow of any failed missions, which are quite likely to happen until you get a better team.

SNAKEMAN provides Levels at the cost of Ryo, but this effect is negligible since most Outskirts mission only give around 10 Ryo. It is also negated by Haus's effect (does not require a team up bonus, so third party member is allowed).

proof-reader Requires S4+ and the sacrifice of multiple note pages to acquire. Even if you aren't completely done with the wasteland by the time you acquire him, you could employ him for his +1 to range. Having a valuable ally drop sweetens the deal for high level players running wasteland missions.

sporty-lvl-2 does not provide any bonus in the wasteland, she is considered a wasteland ally and will not be disabled in wasteland missions. This is useful if you are trying to get her ally drop item.

A team of Haus + SNAKEMAN + either Terri Lvl 2 or Mr Sandman is best to get started.

Jutsu & Reaper Blood

Learning Haus's Jutsu Inner Monologue is very useful. Even with the 10x Chakra costs in the Outskirts, it's only 30 Chakra for some likely much needed Range. This can also very useful outside of wasteland. Allowing you to tackle S rank missions with a strong strength team, such as Emosuke level 3 and Billy level 3.
Learning Diagnosis can wait until you can form a proper Wasteland team, or if you want a low chakra alternative to Epic Dog Urination Technique.

Get Bones - Unlocks 3a, one of two requirements to unlock 3c

Steps 3a, 3b, and 3c can be done in parallel and in any order. They have different prerequisites, but all are requires for step 4. While in step 2 you will come across various wasteland allies. You need 4 specific ones (referred to as The Four Sounds) in order to unlock higher difficulty wasteland missions. Since Wasteland doesn't allow you to select specific stats, just keep running Outskirts missions until you get the allies you need. You'll be getting drops that you'll need later in addition to the allies you'll want as well. Specifically, you're looking for these four:

Once you've obtained three of these four, you can make the team Three of Four, which may help increase your chances for success in Wasteland. However, you'll need all four to progress. It's a good idea to learn their Jutsus now, especially Flutie's, Sticky's, and Tubby's, as they provide a better Range bonus than Inner Monologue, and for less Chakra, although they only apply to a single attribute. Several of their Jutsu's will be required much later to beat very difficult missions later on in the wasteland.

Once you have all of the Four Sounds (the allies previously mentioned), your next goal is to get Bones. To get Bones, you must get all four of the Four Sounds to Lvl. 2 on the same day. The Four Sounds level up by completing the quest Rock Around the Clock. However, they only remain Lvl. 2 for the remainder of the day; tomorrow they go back to being Lvl. 1 again. Once you have all of the Four Sounds at Lvl. 2, you can begin Battle of the Bands. To complete Battle of the Bands, make sure that you have Emosuke Lvl. 2 (or Emosuke Lvl. 3). Completing this mission will get you Bones, and unlock more difficult missions in Outskirts.

Learn Distilling - Unlock 3b, one of two requirements to unlock 3c

Steps 3a, 3b, and 3c can be done in parallel and in any order. They have different prerequisites, but all are requires for step 4. You learn distilling by completing the special mission Distillation. It unlocks after passing 20 Outskirts missions after you get Haus, which will be easiest if you can gather up a team. Haus will then hit you with another challenge, this time a Ninjutsu 16d4, which should be treated similar to the previous one, but you may have access to some Wasteland allies by now to help. After this, Haus will ask you to brew 10 potions of various kinds. Any will do (you can brew 10 Potion Bases or 10 Super Potions or any combination of anything, it doesn't matter). This will add a workshop link to the main page, unlock the distill interface, and give you basic-blueprints. Which are necessary for Wasteland item crafting.

Step 3b - Cloak, Pistol, and Scythe.

At this point in time you will need to start crafting your unique wasteland gear.

There are 6 wasteland item types total, and multiple items can qualify for each type. Different item types are crafted at different steps.

The most powerful of each item type requires that you use a magic rune, you cannot use magic runes in crafting until you do the quest runic-blueprints, which requires that you be season 3. Don't let this discourage you from doing the wasteland in season 1 and 2. It is quite doable and there is no real benefit for waiting. Crafting the final items can take a long time to acquire the components for and usually rewards you with a benefit that can be used even outside of the wasteland itself.

Wasteland items's bonuses do not stack with other wasteland items of the same category.

The item requirements can also be satisfied by some specific items which are acquired rather then crafted, the benefit those items give you stack with each other and with your most powerful wasteland item.

You only need one Cloak of any kind to proceed to the next step.
Perhaps the most urgent of the Wasteland items that you'll want is a Cloak. Cloaks reduce the stamina penalty from doing Wasteland missions, and so getting a cloak early means you'll be able to run more Wasteland missions for less stamina. This is only useful if you don't already have the item Survived the Impossible which completely eliminates wasteland stamina drain.
See Wasteland Recipes Step-By-Step page for a complete set of instructions on what is needed for each part, and how to assemble the ingredients.

Crafted Wasteland Cloaks listed from 'best' to 'worst' (only best bonus applies, bonuses do not stack):

Step 4 - Unlock Wasteland

Once you have obtained Good Boy and have completed 100 Outskirts missions, you unlock the quest Field Trip. This is why you've been collecting and creating the various items from Outskirts. To pass Field Trip, you will need a Cloak, a Pistol, a Scythe, and Shades. Once you've presented these items, you will need to be 'alone'. This requires that you have 20 or less stamina, no teammates and not hanging out with anyone. Once you pass this point, you obtain The Cote and now have access to Wasteland missions!

NOTE: To obtain Chunks, and complete any further parts of the wastelands, you must be at least Jonin as two of Chunk's pieces are located in A-Rank missions.

During your various Wasteland missions, you'll probably come across a Disembodied Head from a Gen 20/8 mission. This unlocks the quest for Chunks. To get Chunks you must track down the rest of his body parts while still on the quest Chunks. His body parts can be found on the following missions:

Once you've obtained Jaws, Venus and Chunks, you unlock the quest The Paper. To complete this mission, you will need 10 Note Pages. Once you've given up these pages, you will construct a Ninja out of the pages and obtain The Paper.
Rather than collecting the pages one by one from missions, you may want to consider using a few in bingo-ing to get Hyuk from TheTrade and looting them from his drops.
You can technically complete step 6 before finishing step 5, since only 3 of the four allies from step 5 are needed.

The next step of Wasteland is to get Threads, which is done through the infamous process of kicking junk. There are four Junk quests that you must do, in a specific order. To unlock them, you must have the required ally (or allies) in your party for the mission to unlock. (Bones, Paper & Mr. Sandman works for the first three Junk quests). Thus to proceed you should put the following allies in your party in the following order:

*Note* You can switch allies in your team if you have problems with the quest, just make sure you start the quest first then swap teammates!
After you have kicked these four junks, you can now complete Junk Showdown, which will get you Threads. You're almost done with the first part of Inner Wasteland!

Once you have Threads and one Note Page, you can proceed to what is generally referred to as 'Inner Inner Wasteland', or the more advanced Wasteland missions. Having Threads will unlock the quest Second Opinion. The main requirement for this mission is a Silver Scythe or better (such as a Wasteland Scythe). Once you have completed this mission, you can now do Inner Inner Wasteland missions, and you're just about in the home stretch.

Step 9 - Inner Inner Wasteland

You only need one pair of boots of any kind to proceed to the next step.
Once you have access to Inner Inner Wasteland, you gain access to fur, which will be used to make the next items you need to progress.
Boots provide you with some amount of chakra back whenever you complete a mission (including non wasteland missions), making them a wonderful item.

Crafted Wasteland Boots listed from 'best' to 'worst' (only best bonus applies, bonuses do not stack)

You only need one cowl of any kind to proceed to the next step.
Perhaps the most important item after you complete Wasteland will be your cowl. Your cowl powers up your Storm's power later on for the Eye of the Storm bloodline. The better the cowl, the more powerful your storm.

Crafted Wasteland Cowls listed from 'best' to 'worst' (only best bonus applies, bonuses do not stack)

Once you get to Inner Inner Wasteland, you can level up Mr. Sandman and Terri Lvl. 2. This is completely optional, however, you should do it at some time. Mr. Sandman Lvl. 2 has an incredible jutsu for bingo'ing, and it would be really hard to turn down. Terri Lvl. 3 will make it significantly easier to get monster drops in the future if you're not a Kage. They can be leveled up on the following missions:

You need the ability to pass a Nin 25d/25s challenge using only Wasteland abilities

You need to hang out with a full team which does not have to be wasteland allies. This is now simpler than ever, simply use the triple walrus from the akatsuki ball in the party house. Alternative you could find 3 rather unpopular teammates and work them the day before2. If you are short on unpopular teammates you could also buy a MOME from the arena or the market to guarantee hanging out with a popular teammate. You could also use Floating On Air, but its likely to be more costly then any alternative by this point.

To overcome the Nin 25d/25s challenge use a team of Sticky Level 2, Palmface and Venus. Your Reaper blood state should be set to either Bankai or Cobra Kai, depending on your stats from other sources. Reaper Blood Shikai is useless for this quest. Use along with your best Nin Wasteland Jutsu (such as Rock On: Webslinger or Rock On: Spider Man.
It helps if you used crafted wasteland shades due to their strength bonus actually working in the wasteland. It also helps to have +success item from the arena, any +success or +Nin levels item you can get your hands on. Also have the Knightmare Frame and be max level for your season. You can retry this mission several times in one day if you fail, just remember that each use of Rock On: Spinal Tap takes an Emo Rock CD, so it'd be prudent to have a stock.
If you can't do all of these, just do the best you can. Consult the Success Calculator to see if you are ready to attempt this quest.